Time–frequency analysis

About: Time–frequency analysis is a research topic. Over the lifetime, 5407 publications have been published within this topic receiving 104346 citations.

Adaptive SVD based AR model order determination for time frequency analysis of Doppler ultrasound signals

Abstract: The short-time Fourier transform provides a picture of the spectral components temporal location in time-varying signals, but its performance is limited by the intrinsic trade-off between time and frequency resolutions. In the present study, this problem is addressed using a spectral estimator based on a combination of the autoregressive (AR) modeling technique and a new automatic model order selection method. The order estimation is achieved by means of the singular value decomposition (SVD) of an appropriate data matrix in conjunction with a new criterion (dynamic mean evaluation, DME). The latter is used to decide which singular values correspond to the signal and which to the noise subspaces, avoiding an a priori threshold definition, thus giving the variable AR model order on consecutive short-time segments. Combination of the AR high frequency resolution capabilities and the SVD plus DME robustness and simplicity make the overall method reliable in many practical applications, mainly in the analysis of time-varying signals corrupted by noise. The proposed procedure has been applied to benchmark as well as to Doppler signal analysis. Some examples are reported confirming the above-mentioned properties.

Novel DCT-Based Real-Valued Discrete Gabor Transform and Its Fast Algorithms

Abstract: The oversampled Gabor transform is more effective than the critically sampled one in many applications. The biorthogonality relationship between the analysis window and the synthesis window of the Gabor transform represents the completeness condition. However, the traditional discrete cosine transform (DCT)-based real-valued discrete Gabor transform (RGDT) is available only in the critically sampled case and its biorthogonality relationship for the transform has not been unveiled. To bridge these important gaps, this paper proposes a novel DCT-based RDGT, which can be applied in both the critically sampled case and the oversampled case, and their biorthogonality relationships can be derived. The proposed DCT-based RDGT involves only real operations and can utilize fast DCT algorithms for computation, which facilitates computation and implementation by hardware or software as compared to that of the traditional complex-valued discrete Gabor transform. This paper also develops block time-recursive algorithms for the efficient and fast computation of the RDGT and its inverse transform. Unified parallel lattice structures for the implementation of these algorithms are presented. Computational complexity analysis and comparisons have shown that the proposed algorithms provide a more efficient and faster approach for discrete Gabor transforms as compared to those of the existing discrete Gabor transform algorithms. In addition, an application in the noise reduction of the nuclear magnetic resonance free induction decay signals is presented to show the efficiency of the proposed RDGT for time-frequency analysis.

Toward High-Quality Real-Time Signal Reconstruction From STFT Magnitude

Abstract: An efficient algorithm for real-time signal reconstruction from the magnitude of the short-time Fourier transform (STFT) is introduced. The proposed approach combines the strengths of two previously published algorithms: the real-time phase gradient heap integration and the Gnann and Spiertz's real-time iterative spectrogram inversion with look-ahead. An extensive comparison with the state-of-the-art algorithms in a reproducible manner is presented.

Wavelet and matching pursuit estimates of the transient-evoked otoacoustic emission latency.

Abstract: Different time–frequency techniques may be used to investigate the relation between latency and frequency of transient-evoked otoacoustic emissions. In this work, the optimization of these techniques and the interpretation of the experimental result are discussed. Time–frequency analysis of click-evoked otoacoustic emissions of 42 normal-hearing young subjects has been performed, using both wavelet and matching pursuit algorithms. Wavelet techniques are very effective to provide fast and reliable evaluation of the average latency of large samples of subjects. A major advantage of the matching pursuit technique, as observed by Jedrzejczak et al. [J. Acoust. Soc. Am. 115, 2148–2158 (2004)], is to provide detailed information about the time evolution of the response of single ears at selected frequencies. A hybrid matching pursuit algorithm that includes Fourier spectral information was developed, capable of speeding-up computation times and of identifying “spurious” atoms, whose latency-frequency relation i...

Interference analysis of multicarrier systems based on affine fourier transform

Abstract: Multicarrier techniques based on affine Fourier transform (AFT) have been recently proposed for transmission in the wireless channels. The AFT represents a generalization of the Fourier and fractional Fourier transform. We derive the exact and approximated interference power, upper bound and measure of applicability for the AFT based multicarrier (AFT-MC) system. It is demonstrated that the AFT-MC system effectively minimizes interference in time-varying multipath channels with line-of-sight component and narrow beamwidth of scattered components that often occurs in aeronautical and satellite communications.